A Characterization of Similarity Maps Between Euclidean Spaces Related to the Beckman--Quarles Theorem

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dc.creatorHeitzig, Jobst
dc.date2002-03-22
dc.date.accessioned2026-07-07T04:47:14Z
dc.date.available2026-07-07T04:47:14Z
dc.descriptionIt is shown that each continuous transformation $h$ from Euclidean $m$-space ($m>1$) into Euclidean $n$-space that preserves the equality of distances (that is, fulfils the implication $|x-y|=|z-w|\Rightarrow|h(x)-h(y)|=|h(z)-h(w)|$) is a similarity map. The case of equal dimensions already follows from the Beckman--Quarles Theorem.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/math/0203233
dc.identifierhttp://arxiv.org/abs/math/0203233
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63632
dc.subjectMetric Geometry
dc.subjectGeneral Topology
dc.subject51F20; 51F25; 15A04
dc.titleA Characterization of Similarity Maps Between Euclidean Spaces Related to the Beckman--Quarles Theorem
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